<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0370-3908</journal-id>
<journal-title><![CDATA[Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. acad. colomb. cienc. exact. fis. nat.]]></abbrev-journal-title>
<issn>0370-3908</issn>
<publisher>
<publisher-name><![CDATA[Academia Colombiana de Ciencias Exactas, Físicas y Naturales]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0370-39082020000100142</article-id>
<article-id pub-id-type="doi">10.18257/raccefyn.965</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Determinación del espectro de energía de un haz de rayos X terapéutico de kilovoltaje a partir de su curva de atenuación]]></article-title>
<article-title xml:lang="en"><![CDATA[Determination of energy spectrum of a therapeutic kilovoltage X-ray beam from its attenuation curve]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gonçalves]]></surname>
<given-names><![CDATA[Ana Carolina]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Wilches Visbal]]></surname>
<given-names><![CDATA[Jorge Homero]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Da Costa]]></surname>
<given-names><![CDATA[Alessandra Martins]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de São Paulo Departamento de Física ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Brazil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad del Magdalena Facultad de Ciencias de la Salud ]]></institution>
<addr-line><![CDATA[Santa Marta ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2020</year>
</pub-date>
<volume>44</volume>
<numero>170</numero>
<fpage>142</fpage>
<lpage>152</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0370-39082020000100142&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0370-39082020000100142&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0370-39082020000100142&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Muchas áreas científicas y tecnológicas asociadas a procesos industriales, radiodiagnóstico y terapia radiante demandan altos niveles de precisión y practicidad en la medición de espectros de energía de rayos X. El espectro de un haz de rayos X puede determinarse de manera directa, a través de un detector de alta resolución, o de manera indirecta utilizando su curva de atenuación y una apropiada técnica matemática. La medición directa del espectro de rayos X suele ser costosa, problemática y exige considerable experticia. El propósito del presente trabajo fue determinar el espectro de energía de un haz de rayos X de kilovoltaje (kV) utilizando una medición indirecta del mismo, basada en la curva de atenuación del haz y en el uso de transformadas de Laplace. Para esto, i) se llevó a cabo una descripción completa y exhaustiva de la derivación matemática de la función que representa al espectro de energía; ii) se reconstruyó el espectro usando el algoritmo multistart junto con la función lsqnonlin de MATLAB; iii) se validó la reconstrucción del espectro comparando los valores de la capa semirreductora del espectro y de la curva de atenuación. Los resultados mostraron que los valores de las capas semirreductoras del espectro y la curva de atenuación fueron próximos entre sí y que el tiempo de cálculo del espectro fue notablemente corto. Por tanto, se concluye que la determinación indirecta del espectro de rayos X a partir de su curva de atenuación y mediante el uso novedoso de la sinergia multistart-lsqnonlin, es una alternativa más simple, más rápida y tan eficaz como la de medición directa del espectro.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract Many scientific and technological areas associated with industrial process, diagnostic radiation images and radiation therapy demand high levels of accuracy and practicality for the measurement of X-ray energy spectra. The energy spectra of an X-ray beam can be determined either a direct or indirect measurement. Direct measurement uses a high energy resolution detector placed along the direction of the beam. Indirect measurement is based on the transmission curve of the beam and Laplace transforms. For this, i) a complete and exhaustive description of the mathematical derivation of the energy spectrum was carried out; ii) it was used the multistart algorithm along with the lsqnonlin function of MATLAB for the reconstruction of the spectrum; iii) the reconstruction of the spectrum was validated by comparing the half-value layer of the spectrum and the attenuation curve. The results showed that the half-value layer values of the spectrum and the attenuation curve were close to each other and the calculation time of the spectrum was considerably short. Therefore, it is concluded that the indirect determination of the X-ray spectrum from its attenuation curve by means of the novelty usage of the multistart-lsqnonlin synergy is a demonstrably simpler, faster and as effective alternative as the direct spectrum measurement.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Espectroscopia]]></kwd>
<kwd lng="es"><![CDATA[Rayos X]]></kwd>
<kwd lng="es"><![CDATA[Transformadas de Laplace]]></kwd>
<kwd lng="es"><![CDATA[Transmisión;Radioterapia]]></kwd>
<kwd lng="es"><![CDATA[Radiología]]></kwd>
<kwd lng="en"><![CDATA[Spectroscopy]]></kwd>
<kwd lng="en"><![CDATA[X-ray]]></kwd>
<kwd lng="en"><![CDATA[Laplace transforms]]></kwd>
<kwd lng="en"><![CDATA[Transmission]]></kwd>
<kwd lng="en"><![CDATA[Radiotherapy]]></kwd>
<kwd lng="en"><![CDATA[Radiology]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Abbene]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Gerardi]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Principato]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Del Sordo]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Raso]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Direct measurement of mammographic x-ray spectra with a digital CdTe detection system]]></article-title>
<source><![CDATA[Sensors]]></source>
<year>2012</year>
<volume>12</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>8390-404</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[AL-Jasim]]></surname>
<given-names><![CDATA[A. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Hulugalle]]></surname>
<given-names><![CDATA[S. N. C. W. M. P. S. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Al-Hamadani]]></surname>
<given-names><![CDATA[H. K]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A Quality Control Test for General X-Ray Machine]]></article-title>
<source><![CDATA[World Scientific News]]></source>
<year>2017</year>
<volume>90</volume>
<page-range>11-30</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Archer]]></surname>
<given-names><![CDATA[B. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Wagner]]></surname>
<given-names><![CDATA[L. K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A Laplace transform pair model for spectral reconstruction]]></article-title>
<source><![CDATA[Medical physics]]></source>
<year>1982</year>
<volume>9</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>844-7</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Archer]]></surname>
<given-names><![CDATA[B. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Wagner]]></surname>
<given-names><![CDATA[L. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Johnston]]></surname>
<given-names><![CDATA[D. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Almond]]></surname>
<given-names><![CDATA[P. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Bushong]]></surname>
<given-names><![CDATA[S. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Analysis of errors in spectral reconstruction with a Laplace transform pair model]]></article-title>
<source><![CDATA[Physics in Medicine &amp; Biology]]></source>
<year>1985</year>
<volume>30</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>411</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Archer]]></surname>
<given-names><![CDATA[B. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Wagner]]></surname>
<given-names><![CDATA[L. K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Determination of diagnostic x-ray spectra with characteristic radiation using attenuation analysis]]></article-title>
<source><![CDATA[Medical physics]]></source>
<year>1988</year>
<month>a</month>
<volume>15</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>637-41</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Archer]]></surname>
<given-names><![CDATA[B. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Wagner]]></surname>
<given-names><![CDATA[L. K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A modified x-ray spectra reconstruction technique]]></article-title>
<source><![CDATA[Physics in Medicine &amp; Biology]]></source>
<year>1988</year>
<month>b</month>
<volume>33</volume>
<numero>12</numero>
<issue>12</issue>
<page-range>1399</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Attix]]></surname>
<given-names><![CDATA[F. H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Introduction to radiological physics and radiation dosimetry]]></source>
<year>2008</year>
<publisher-name><![CDATA[John Wiley &amp; Sons]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ay]]></surname>
<given-names><![CDATA[M. R.]]></given-names>
</name>
<name>
<surname><![CDATA[Shahriari]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sarkar]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Adib]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Zaidi]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Monte Carlo simulation of x-ray spectra in diagnostic radiology and mammography using MCNP4C]]></article-title>
<source><![CDATA[Physics in Medicine &amp; Biology]]></source>
<year>2004</year>
<volume>49</volume>
<numero>21</numero>
<issue>21</issue>
<page-range>4897</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Baird]]></surname>
<given-names><![CDATA[L. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[X-ray spectra vs attenuation data: A theoretical analysis]]></article-title>
<source><![CDATA[Medical physics]]></source>
<year>1981</year>
<volume>8</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>319-23</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bell]]></surname>
<given-names><![CDATA[G. E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Spectral distribution in the continuous X-ray spectrum and the specification of X-ray quality]]></article-title>
<source><![CDATA[The British Journal of Radiology]]></source>
<year>1936</year>
<volume>9</volume>
<numero>106</numero>
<issue>106</issue>
<page-range>680-8</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bilge]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Beam characteristics of kilovoltage radiotherapy unit]]></article-title>
<source><![CDATA[Journal of BU ON.: official journal of the Balkan Union of Oncology]]></source>
<year>2004</year>
<volume>9</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>303-6</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bonifácio]]></surname>
<given-names><![CDATA[D. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Murata]]></surname>
<given-names><![CDATA[H. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Moralles]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Monte Carlo Simulation of X-ray spectra in diagnostic radiology and mammography using Geant4]]></source>
<year>2005</year>
<conf-name><![CDATA[ International Nuclear Atlantic Conference]]></conf-name>
<conf-date>2005</conf-date>
<conf-loc> </conf-loc>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bos]]></surname>
<given-names><![CDATA[A. J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Fundamentals of radiation dosimetry]]></article-title>
<source><![CDATA[AIP Conference Proceedings]]></source>
<year>2011</year>
<volume>1345</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>5-23</page-range><publisher-name><![CDATA[AIP]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[S. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Jong]]></surname>
<given-names><![CDATA[W. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Harun]]></surname>
<given-names><![CDATA[A. Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Evaluation of x-ray beam quality based on measurements and estimations using SpekCalc and IPEM78 models]]></article-title>
<source><![CDATA[The Malaysian journal of medical sciences: MJMS]]></source>
<year>2012</year>
<volume>19</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>22</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Correa]]></surname>
<given-names><![CDATA[E. D. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Vivolo]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Potiens]]></surname>
<given-names><![CDATA[M. D. P. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Determination of the effective energy in X-rays standard beams, mammography level]]></source>
<year>2012</year>
<publisher-loc><![CDATA[Brazil ]]></publisher-loc>
<publisher-name><![CDATA[Instituto de Pesquisas Energéticas e Nucleares]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[De la Vega J]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Guirado]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Vilches]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Perdices]]></surname>
<given-names><![CDATA[J. I.]]></given-names>
</name>
<name>
<surname><![CDATA[Lallena]]></surname>
<given-names><![CDATA[A. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Obtaining the intrinsic electron spectrum of linear accelerators using the relation between the current of the bending magnet and the absorbed dose in water]]></article-title>
<source><![CDATA[Radiotherapy and Oncology]]></source>
<year>2008</year>
<volume>86</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>109-13</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Comparison between measured and predicted attenuation curves of x-ray beams]]></article-title>
<source><![CDATA[Medical physics]]></source>
<year>1999</year>
<volume>26</volume>
<numero>10</numero>
<issue>10</issue>
<page-range>2183-9</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Determination of x-ray spectra from attenuation data by imposing a priori positiveness and bounded support: Theory and experimental validation]]></article-title>
<source><![CDATA[Medical physics]]></source>
<year>2007</year>
<volume>34</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>994-1006</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Determination of x-ray spectra from Al attenuation data by imposing a priori physical features of the spectrum: Theory and experimental validation]]></article-title>
<source><![CDATA[Medical physics]]></source>
<year>2009</year>
<volume>36</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>142-8</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dodson]]></surname>
<given-names><![CDATA[C. T. J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Introduction to laplace transforms for engineers. School of Mathematics]]></source>
<year>2002</year>
<publisher-name><![CDATA[Manchester University Lecture Notes]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dossel]]></surname>
<given-names><![CDATA[O.]]></given-names>
</name>
<name>
<surname><![CDATA[Schlegel]]></surname>
<given-names><![CDATA[W. C.]]></given-names>
</name>
</person-group>
<source><![CDATA[World Congress on Medical Physics and Biomedical Engineering September 7-12, 2009 Munich, Germany: Vol. 25/IX Neuroengineering, Neural Systems, Rehabilitation and Prosthetics (Vol. 25)]]></source>
<year>2010</year>
<publisher-name><![CDATA[Springer Science &amp; Business Media]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dyson]]></surname>
<given-names><![CDATA[N. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Dyson]]></surname>
<given-names><![CDATA[N. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[X-rays in Atomic and Nuclear Physics]]></source>
<year>2005</year>
<publisher-name><![CDATA[Cambridge University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Glover]]></surname>
<given-names><![CDATA[J. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Chantler]]></surname>
<given-names><![CDATA[C. T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A method to determine the absolute harmonic content of an X-ray beam using attenuation measurements]]></article-title>
<source><![CDATA[X-Ray Spectrometry: An International Journal]]></source>
<year>2009</year>
<volume>38</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>510-2</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kramer]]></surname>
<given-names><![CDATA[H. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Von Seggern]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The determination of x-ray spectra from attenuation data: Part I: The potentials of various methods]]></article-title>
<source><![CDATA[Nuclear Instruments and Methods in Physics Research]]></source>
<year>1983</year>
<volume>213</volume>
<numero>2-3</numero>
<issue>2-3</issue>
<page-range>373-80</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kramer]]></surname>
<given-names><![CDATA[H. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The determination ofx-ray spectra from attenuation data: Part II: Experimental results]]></article-title>
<source><![CDATA[Nuclear Instruments and Methods in Physics Research]]></source>
<year>1983</year>
<volume>214</volume>
<numero>2-3</numero>
<issue>2-3</issue>
<page-range>445-50</page-range></nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Wu]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Lin]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Wu]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<source><![CDATA[Electron spectrum reconstruction as nonlinear programming model using micro-adjusting algorithm]]></source>
<year>2008</year>
<conf-name><![CDATA[ 7thAsian-Pacific Conference on Medical and Biological Engineering]]></conf-name>
<conf-loc>Berlin, Heidelberg </conf-loc>
</nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ma]]></surname>
<given-names><![CDATA[C. C.]]></given-names>
</name>
</person-group>
<source><![CDATA[AAPM. Measurement of radiation, Fox Chase Cancer Center, Philadelphia, PA, USA]]></source>
<year>2014</year>
</nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mainardi]]></surname>
<given-names><![CDATA[R. T.]]></given-names>
</name>
<name>
<surname><![CDATA[Bonzi]]></surname>
<given-names><![CDATA[E. V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An indirect method of X-ray spectra measurement by simultaneous attenuations of the scattered beam]]></article-title>
<source><![CDATA[Radiation Physics and Chemistry]]></source>
<year>2008</year>
<volume>77</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>537-44</page-range></nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Malezan]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Tomal]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Antoniassi]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Watanabe]]></surname>
<given-names><![CDATA[P. C. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Albino]]></surname>
<given-names><![CDATA[L. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Poletti]]></surname>
<given-names><![CDATA[M. E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Spectral reconstruction of dental X-ray tubes using laplace inverse transform of the attenuation curve]]></article-title>
<source><![CDATA[Radiation Physics and Chemistry]]></source>
<year>2015</year>
<volume>116</volume>
<page-range>278-81</page-range></nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Menin]]></surname>
<given-names><![CDATA[O. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Martinez]]></surname>
<given-names><![CDATA[A. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Costa]]></surname>
<given-names><![CDATA[A. M. D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Reconstruction of bremsstrahlung spectra from attenuation data using generalized simulated annealing]]></article-title>
<source><![CDATA[Applied Radiation and Isotopes]]></source>
<year>2016</year>
<volume>111</volume>
<page-range>80-5</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nickoloff]]></surname>
<given-names><![CDATA[E. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Berman]]></surname>
<given-names><![CDATA[H. L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Factors affecting x-ray spectra]]></article-title>
<source><![CDATA[Radiographics]]></source>
<year>1993</year>
<volume>13</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1337-48</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Panthi]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Determination of the Energy Spectra of Clinical X-Ray Beams Using Dose-Depth Datasets]]></source>
<year>2018</year>
<publisher-name><![CDATA[Oklahoma State University]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pamplona]]></surname>
<given-names><![CDATA[G. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Costa]]></surname>
<given-names><![CDATA[A. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Determinação do espectro de raios X a partir da curva de transmissão para um equipamento de radiografia dentária]]></article-title>
<source><![CDATA[Revista Brasileira de Física Médica]]></source>
<year>2010</year>
<volume>4</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>23-5</page-range></nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Pernicka]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[McLean]]></surname>
<given-names><![CDATA[I. D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Dosimetry in diagnostic radiology: an international code of practice]]></source>
<year>2007</year>
<publisher-name><![CDATA[International Atomic Energy Agency]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Poludniowski]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Landry]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[DeBlois]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Evans]]></surname>
<given-names><![CDATA[P. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Verhaegen]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[SpekCalc: a program to calculate photon spectra from tungsten anode x-ray tubes]]></article-title>
<source><![CDATA[Physics in Medicine &amp; Biology]]></source>
<year>2009</year>
<volume>54</volume>
<numero>19</numero>
<issue>19</issue>
<page-range>N433</page-range></nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Santos]]></surname>
<given-names><![CDATA[J. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Gonzales]]></surname>
<given-names><![CDATA[A. H. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Terini]]></surname>
<given-names><![CDATA[R. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Costa]]></surname>
<given-names><![CDATA[P. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Determinação da camada semirredutora e da tensão aplicada a partir de espectros emitidos por um tubo de raios X]]></article-title>
<source><![CDATA[Revista Brasileira de Física Médica]]></source>
<year>2016</year>
<volume>10</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>28-33</page-range></nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Silberstein]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[XXXIV. Spectral composition of an X-ray radiation determined from its filtration curve]]></article-title>
<source><![CDATA[The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science]]></source>
<year>1933</year>
<volume>15</volume>
<numero>98</numero>
<issue>98</issue>
<page-range>375-94</page-range></nlm-citation>
</ref>
<ref id="B38">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Smith]]></surname>
<given-names><![CDATA[F. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[A primer in applied radiation physics]]></source>
<year>2000</year>
<publisher-name><![CDATA[World Scientific Publishing Company]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B39">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Twidell]]></surname>
<given-names><![CDATA[J. W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The determination of X-ray spectra using attenuation measurements and a computer program]]></article-title>
<source><![CDATA[Physics in Medicine &amp; Biology]]></source>
<year>1970</year>
<volume>15</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>529</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
